Mint Lollipops

Lightly oil 2 large baking sheets.
Bring water to a boil in a 1-quart heavy saucepan, then stir in mint and remove from heat. Cool slightly, about 2 minutes, then purée in a blender, about 1 minute (use caution when blending hot liquids). Strain through a fine-mesh sieve lined with 2 layers of paper towel into a bowl, pressing on and then discarding solids (you should have at least 2/3 cup liquid).
Have an ice bath ready.
Heat sugar, corn syrup, and 2/3 cup mint liquid in cleaned saucepan over medium heat, stirring, until sugar has dissolved. Bring to a boil over medium heat, without stirring, washing any sugar crystals down side of pan with a pastry brush dipped in cold water and skimming any foam from surface. Put thermometer into syrup and boil until it registers 300°F (hard-crack stage), then stir in mint extract. Immediately dip bottom of pan in ice bath to stop cooking.
Pour a 2-inch pool of syrup onto 1 of the baking sheets and quickly put a lollipop stick in it. Continue making lollipops, spacing pools of syrup 2 inches apart. (If syrup becomes too thick to pour, heat to thin it.) Let lollipops cool and harden, about 15 minutes, then gently loosen with a thin metal spatula. If desired, individually wrap lollipops in cellophane wrappers.